So, the Empire has the science of force fields down to where they can put a personal one into a bracelet and it will protect you from a lot.
But when the imperial ship come to Terminus, and somehow it can't look down and see these big cannons out in plan sight--it takes just one blast from one of those cannons to take out the whole huge ship (some writer of this show saw Star Wars too many times. Big ships can always be made to explode with one well aimed shot, apparently),
But are you seriously telling me this ship had no force field? Why not? Would that be standard for an imperial ship?
Oh, and the force fields also go down in the town and they've no back up. 🙄 Are the force fields like wifi? They go down that easily?
"The fields are down! The barbarians are entering and slaughtering everyone! Damn you Spectrum!'
Shouldn't there be a back-up generator?
Some physicists believe it may not actually be possible without changing its properties They say they have reached a lab report writer in the local force field. Science fiction often anticipates real technology.
The force field of the Foundation is then "whatever it is that protects the Foundation".
You have a point that force fields are rather confusing in the series. They certainly don't look like any sort of physical technology that could conceivably be developed in the future. In good old-fashioned SF, force fields were roughly spherical, as you would expect of any physical effect. In the series, the Emperor has a force field that somehow follows the contours of his body, and to add to the implausibility, comes from a bracelet.
So probably a better interpretation of the force field is "whatever it is that protects the Emperor". With that point of view, it makes sense that individual imperial ships don't have it. The Imperial Space Force as a whole may be part of what is protecting the Empire, but no individual ship has the force field.
The force field of the Foundation is then "whatever it is that protects the Foundation". And to the question of whether there is any backup, I think we'll find out when Gaal gets to Helicon, whether that's some sort of backup to the Foundation or what.